12/11/2018
Content
Background
- Titanic is a famous movie released in 1997.
- It is a romantic and sad love story.
Background
- Behind the movie, Titanic sinking is a real event happened in 1912 because of colliding with an iceberg.
- It is a big disaster more than 1500 people dead while Titanic had an estimated 2,224 people on board.
Question design and data source
- Question
Some groups of people were more likely to survive than others, so we design the question on analyzing what factors lead to the survive/loss of passengers and crews based on their information.
- Data source
Dataset overview
## 'data.frame': 891 obs. of 12 variables: ## $ PassengerId: int 1 2 3 4 5 6 7 8 9 10 ... ## $ Survived : int 0 1 1 1 0 0 0 0 1 1 ... ## $ Pclass : int 3 1 3 1 3 3 1 3 3 2 ... ## $ Name : Factor w/ 891 levels "Abbing, Mr. Anthony",..: 109 191 358 277 16 559 520 629 417 581 ... ## $ Sex : Factor w/ 2 levels "female","male": 2 1 1 1 2 2 2 2 1 1 ... ## $ Age : num 22 38 26 35 35 NA 54 2 27 14 ... ## $ SibSp : int 1 1 0 1 0 0 0 3 0 1 ... ## $ Parch : int 0 0 0 0 0 0 0 1 2 0 ... ## $ Ticket : Factor w/ 681 levels "110152","110413",..: 524 597 670 50 473 276 86 396 345 133 ... ## $ Fare : num 7.25 71.28 7.92 53.1 8.05 ... ## $ Cabin : Factor w/ 148 levels "","A10","A14",..: 1 83 1 57 1 1 131 1 1 1 ... ## $ Embarked : Factor w/ 4 levels "","C","Q","S": 4 2 4 4 4 3 4 4 4 2 ...
\(Survived\)
0=No, 1=Yes
\(Pclass\)
Ticket class 1st=upper, 2nd=Middle, 3rd=lower
Dataset overview
\(Sibsp\)
siblings / spouses aboard the Titanic
\(Parch\)
parents / children aboard the Titanic
\(Ticket\)
Ticket number
\(Fare\)
Passenger fare
\(Cabin\)
Cabin number
\(Embarked\)
Port of Embarkation, C = Cherbourg, Q = Queenstown, S = Southampton
Data cleansing
We need to check the NA value in variables.
Data cleansing
We use the most frequent values "S" to replace the NA in \(Embarked\).
We use mean of \(Age\) to replace the NA in \(Age\).
We drop \(Cabin\) becuase it has large percentage of NA and least importance.
Data cleansing
- Next, we need to combine some of the variable.
Because \(SibSp\) and \(Parch\) are both the realted family members on board the Titanic.
So we could combine \(SibSp\) and \(Parch\) together to calculate the total family member of this passenger.
Data cleansing
Data cleansing
- Based on the numbers of family member,
we conduct a new factor variable FamilySize, which contains'Single', 'Small', 'Big'.Classification criterion
Single: family member= 0 Small: family member= 1 || family member= 2 Big: family member > 2
## Big Single Small ## 91 537 263
Data cleansing
- We classify age into different AgeGroup.
'Child', 'Juvenile', 'Youth', 'MiddleAge', 'Senium'. Classification criterion
Child: age<= 6 Juvenile: 6< age<= 17 Youth: 17< age<= 40 MiddleAge: 40.5<= age <=65 Senium: age> 65
Data cleansing
EDA
The correlation between variable
EDA
Histogram by group
EDA
Histogram by group
EDA
Histogram by group
EDA
Histogram by group
Logistic regression model
We select \(Survived\) as dependent variable.
Becuase \(Survived\) is binary so we decide to use logistic regression.
Logistic regression model
Initial model
## ## Call: ## glm(formula = Survived ~ Sex + AgeGroup + FamilySize + Pclass + ## Embarked, family = binomial(link = "logit"), data = train) ## ## Deviance Residuals: ## Min 1Q Median 3Q Max ## -2.6809 -0.6706 -0.4057 0.6120 2.4845 ## ## Coefficients: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) 4.00043 0.54265 7.372 1.68e-13 *** ## Sexmale -2.78512 0.20785 -13.400 < 2e-16 *** ## AgeGroupJuvenile -2.07572 0.55559 -3.736 0.000187 *** ## AgeGroupMiddleAge -3.10495 0.51992 -5.972 2.34e-09 *** ## AgeGroupSenium -3.84666 1.20691 -3.187 0.001437 ** ## AgeGroupYouth -2.52134 0.46818 -5.385 7.23e-08 *** ## FamilySizeSingle 1.44313 0.35590 4.055 5.02e-05 *** ## FamilySizeSmall 1.52340 0.35129 4.337 1.45e-05 *** ## Pclass2 -0.98748 0.26969 -3.662 0.000251 *** ## Pclass3 -2.15825 0.25233 -8.553 < 2e-16 *** ## EmbarkedQ -0.04071 0.38457 -0.106 0.915685 ## EmbarkedS -0.43479 0.24216 -1.796 0.072571 . ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## (Dispersion parameter for binomial family taken to be 1) ## ## Null deviance: 1186.66 on 890 degrees of freedom ## Residual deviance: 764.59 on 879 degrees of freedom ## AIC: 788.59 ## ## Number of Fisher Scoring iterations: 5
## (Intercept) Sexmale AgeGroupJuvenile AgeGroupMiddleAge ## 54.62162288 0.06172143 0.12546658 0.04482697 ## AgeGroupSenium AgeGroupYouth FamilySizeSingle FamilySizeSmall ## 0.02135101 0.08035183 4.23394352 4.58780627 ## Pclass2 Pclass3 EmbarkedQ EmbarkedS ## 0.37251559 0.11552692 0.96010289 0.64739747
Logistic regression model
Final model
- We seperate the train dataset into
subtrain dataset (80%)
subvalidation dataset (20%)
- independent variable
\(Pclass\), \(Sex\), \(Age\), \(FamilySize\) - dependent variable
\(Survived\)
Logistic regression model
Final model
## ## Call: ## glm(formula = Survived ~ Sex + AgeGroup + FamilySize + Pclass, ## family = binomial(link = "logit"), data = subtrain) ## ## Deviance Residuals: ## Min 1Q Median 3Q Max ## -2.5330 -0.6091 -0.4544 0.5860 2.4386 ## ## Coefficients: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) 3.1667 0.5613 5.642 1.68e-08 *** ## Sexmale -2.7487 0.2244 -12.250 < 2e-16 *** ## AgeGroupJuvenile -1.6740 0.6380 -2.624 0.008694 ** ## AgeGroupMiddleAge -2.9221 0.6084 -4.803 1.56e-06 *** ## AgeGroupSenium -3.2328 1.2669 -2.552 0.010721 * ## AgeGroupYouth -2.2197 0.5537 -4.009 6.09e-05 *** ## FamilySizeSingle 1.7006 0.4160 4.088 4.35e-05 *** ## FamilySizeSmall 1.7828 0.4101 4.347 1.38e-05 *** ## Pclass2 -0.9727 0.2893 -3.362 0.000773 *** ## Pclass3 -2.1174 0.2670 -7.931 2.17e-15 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## (Dispersion parameter for binomial family taken to be 1) ## ## Null deviance: 954.46 on 712 degrees of freedom ## Residual deviance: 632.72 on 703 degrees of freedom ## AIC: 652.72 ## ## Number of Fisher Scoring iterations: 5
## (Intercept) Sexmale AgeGroupJuvenile AgeGroupMiddleAge ## 23.72803425 0.06401285 0.18748912 0.05382059 ## AgeGroupSenium AgeGroupYouth FamilySizeSingle FamilySizeSmall ## 0.03944646 0.10864363 5.47733010 5.94652228 ## Pclass2 Pclass3 ## 0.37804731 0.12034388
Evaluation
- Next we use the remain 20% data in train dataset to evaluate the model.
## [1] "Accuracy 0.837988826815642"
## [1] 0.8818614
Conclusion
- Our logistic model is good with 0.88 auc, 83.8% classification accuracy.
- The ROC curve also look nice.
- The variable \(Sex\), \(AgeGroup\), \(FamilySize\), \(Pclass\) have significant statistic relationship with \(Survived\).
- Passenger/crew who is female, Child, in class 1, in small size family are more likely to survive.
Conclusion
Conclusion
Thank you!